- #1

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## Main Question or Discussion Point

If so, wouldn't gamma would be like?

(1 - w^2 / c^2)^-1/2

or

(1 - v^2 / r^2c^2)^-1/2

(1 - w^2 / c^2)^-1/2

or

(1 - v^2 / r^2c^2)^-1/2

- Thread starter zeromodz
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- #1

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If so, wouldn't gamma would be like?

(1 - w^2 / c^2)^-1/2

or

(1 - v^2 / r^2c^2)^-1/2

(1 - w^2 / c^2)^-1/2

or

(1 - v^2 / r^2c^2)^-1/2

- #2

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Your first expression must be incorrect because c has units length/time, and w presumable has units 1/time since I'm guessing it is an angular velocity. So w^2/c^2 is not dimensionless as it should be since it is subtracted from the dimensionless quantity 1.

The same goes for the second expression, v^2/(r^2*c^2) is not dimensionless if v is an ordinary velocity of dimension length/time, and r is a length.

Consider a particle moving in a circle at radius r with a tangential velocity v. The gamma factor you'd get in your expressions would still be

gamma = 1/sqrt(1-v^2/c^2)

But if you want you may express it in terms of an angular velocity w by defining w := v/r and then you get

gamma = 1/sqrt(1- w^2*r^2/c^2)

Or you could use some factors of Pi if you like in your definition of the angular velocity. They would then appear in gamma aswell.

- #3

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Thnking about relativistic angular velocity can lead to some interesting conclusions e.g. about the nature of electron spin.

See for example http://panda.unm.edu/Courses/Finley/P495/TermPapers/relangmom.pdf [Broken]

See for example http://panda.unm.edu/Courses/Finley/P495/TermPapers/relangmom.pdf [Broken]

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- #4

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So that means

Your first expression must be incorrect because c has units length/time, and w presumable has units 1/time since I'm guessing it is an angular velocity. So w^2/c^2 is not dimensionless as it should be since it is subtracted from the dimensionless quantity 1.

The same goes for the second expression, v^2/(r^2*c^2) is not dimensionless if v is an ordinary velocity of dimension length/time, and r is a length.

Consider a particle moving in a circle at radius r with a tangential velocity v. The gamma factor you'd get in your expressions would still be

gamma = 1/sqrt(1-v^2/c^2)

But if you want you may express it in terms of an angular velocity w by defining w := v/r and then you get

gamma = 1/sqrt(1- w^2*r^2/c^2)

Or you could use some factors of Pi if you like in your definition of the angular velocity. They would then appear in gamma aswell.

gamma = 1/sqrt(1- w^2*r^2/c^2)

is the correct formula to use. Also, nobody answered that there really is relativistic angular velocity. Does something way more if it spins really really fast?

- #5

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I think your formula is correct. As for the question, 'does something weigh more if it spins fast', yes it would seem so. Think about angularSo that means

gamma = 1/sqrt(1- w^2*r^2/c^2)

is the correct formula to use. Also, nobody answered that there really is relativistic angular velocity. Does something way more if it spins really really fast?